In the UK there are various checks and balances which would determine eligibility for schooling and healthcare.
Birth's must be registered and Birth Certificates produced to confirm various entitlements. All British subjects have a National Insurance number and National Health Service treatment requires an NHS 'card'.
I am certain that similar systems exist in the US which could be used to identify illegal immigrants, but it seems pretty clear that there is a deliberate desire not to do so.
Like I said - I think the law sounds sensible and it is clearly not racist so long as it applies to EVERYONE.
I do think your earlier sig was bigoted and I think you agreed this in another thread.